Question

A rectangular parking lot has a perimeter of 820ft. The area of the Parking lot measures 42000 ft2. What is the width of the parking lot.

Answer 1

Long story short, the answer is C.) 210

Answer 2

2W + 2L = 820
LW = 42,000 or L = 42,000/W
substitute second equation into first equation:
2W + 2(42,000/W) = 820
2W + 84,000/W = 820
2W^2/W + 84,000/W = 820W/W
2W^2 - 820W + 84,000 = 0
quadratic formula:
W = [820 +/- SQR(672,400 - 4(2)(84,000))]/2(2)
W = [820 +/- 20]/4
W = 200, 210
using second equation:
L = 42,000/200, 42,000/210 = 210, 200
The dimensions of the parking lot are 200ft by 210ft.